How do I add arbitrary metadata to a .dae export?
The collada support built into blender is done using C++ code. I would suggest getting this collada-exporter addon and adjusting it to add in your extra data. You will need to look through the collada specs to see how an extra tag would be acceptable within the file format.

Unless you calculate the tag as you go, you can add a custom property to the object type to store the tag info, then use that in the export steps. You would define that in the addons register()

def register():
    bpy.types.Object.mytag = bpy.props.StringProperty()